Solve lambda^2=2lambda

$$\lambda ^ { 2 } = 2 \lambda$$

Solve for λ

$$\lambda =2$$

$$\lambda =0$$

Steps Using Factoring

Subtract 2\lambda from both sides.

$$\lambda ^{2}-2\lambda =0$$

Factor out \lambda .

$$\lambda \left(\lambda -2\right)=0$$

To find equation solutions, solve \lambda =0 and \lambda -2=0.

$$\lambda =0 \lambda =2$$

Steps Using the Quadratic Formula

Subtract 2\lambda from both sides.

$$\lambda ^{2}-2\lambda =0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, -2 for b, and 0 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$\lambda =\frac{-\left(-2\right)±\sqrt{\left(-2\right)^{2}}}{2}$$

Take the square root of \left(-2\right)^{2}.

$$\lambda =\frac{-\left(-2\right)±2}{2}$$

The opposite of -2 is 2.

$$\lambda =\frac{2±2}{2}$$

Now solve the equation \lambda =\frac{2±2}{2} when ± is plus. Add 2 to 2.

$$\lambda =\frac{4}{2}$$

Divide 4 by 2.

$$\lambda =2$$

Now solve the equation \lambda =\frac{2±2}{2} when ± is minus. Subtract 2 from 2.

$$\lambda =\frac{0}{2}$$

Divide 0 by 2.

$$\lambda =0$$

The equation is now solved.

$$\lambda =2 \lambda =0$$

Steps for Completing the Square

Subtract 2\lambda from both sides.

$$\lambda ^{2}-2\lambda =0$$

Divide -2, the coefficient of the x term, by 2 to get -1. Then add the square of -1 to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$\lambda ^{2}-2\lambda +1=1$$

Factor \lambda ^{2}-2\lambda +1. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(\lambda -1\right)^{2}=1$$

Take the square root of both sides of the equation.

$$\sqrt{\left(\lambda -1\right)^{2}}=\sqrt{1}$$

Simplify.

$$\lambda -1=1 \lambda -1=-1$$

Add 1 to both sides of the equation.

$$\lambda =2 \lambda =0$$